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#Nonlinear Systems

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Santa Fe Institute

The Life and Death of a Drop - C4 Public Lectures

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Explore the fascinating physics of droplet formation, breakup, and splashing, revealing surprising insights into fluid dynamics and their importance in nature and everyday life.
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12 Lesons
54 minutes
On-Demand
Free-Video
Santa Fe Institute

Transient Dynamics - The Key to Ecological Understanding - Alan Hastings, SFI + UC Davis

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Explore transient dynamics in ecology, challenging classical theory focused on long-term behavior. Examine implications for modeling, management, and understanding complex ecological systems.
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12 Lesons
1 hour
On-Demand
Free-Video
Santa Fe Institute

Fluctuations in Complex Network-coupled Oscillators

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Explore the dynamics of network-coupled oscillators, examining fluctuations and their impact on complex systems behavior and stability.
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1 Lesons
45 minutes
On-Demand
Free-Video
MIT OpenCourseWare

Power Electronics: State Space Averaging and Linearization - Lecture 25

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Explore state space averaging for modeling switching converters and linearization of nonlinear averaged models to realize control-to-output transfer functions in power electronics.
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1 Lesons
51 minutes
On-Demand
Free-Video
Instituto de Física Interdisciplinar y Sistemas Complejos (IFISC)

Towards Understanding Social Hysteresis - Insights from Statistical Physics and Surprises

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Explore social hysteresis through statistical physics, uncovering insights and surprises in complex societal dynamics.
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1 Lesons
53 minutes
On-Demand
Free-Video
MonteHeart Lectures

Bifurcations - Troubleshooting

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Enhance your knowledge of bifurcations and their troubleshooting techniques in this insightful lecture on complex systems analysis.
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1 Lesons
49 minutes
On-Demand
Free-Video
Steve Brunton

Drawing Phase Portraits for Nonlinear Systems

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Learn to analyze nonlinear systems by drawing phase portraits, identifying fixed points, linearizing, and inferring global dynamics. Gain practical skills in stability analysis using eigenvalues and eigenvectors.
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7 Lesons
26 minutes
On-Demand
Free-Video
TEDx

Dogonić Teraźniejszość - Mechanizmy Skutecznego Funkcjonowania w Chaotycznej Rzeczywistości

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Poznaj mechanizmy skutecznego funkcjonowania w chaotycznej rzeczywistości. Krzysztof Sarnecki omawia probabilistykę, teorię umiarkowanych zakłóceń, antykruchość i nielinearność jako narzędzia do radzenia sobie z przyszłością.
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1 Lesons
20 minutes
On-Demand
Free-Video
Instituto de Matemática Pura e Aplicada

Turbulência

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Explore os fundamentos da turbulência e suas aplicações na matemática e física com o pesquisador Alexei Maylybaev do IMPA.
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1 Lesons
32 minutes
On-Demand
Free-Video
Steve Brunton

Examples of Nonlinear Systems - Particle in a Potential Well

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Explore nonlinear systems through the particle in a potential well example, covering Euler-Lagrange equations, vector fields, phase portraits, and damping in engineering mathematics.
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10 Lesons
50 minutes
On-Demand
Free-Video
ICTP Mathematics

Stabilization of Nonlinear Systems by Oscillating Controls with Application

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Explore nonlinear system stabilization using oscillating controls, with applications in nonholonomic and fluid dynamics. Covers control design, Lie brackets, and energy cascades.
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16 Lesons
1 hour
On-Demand
Free-Video
Fields Institute

Tame Control Theory - Lecture 5

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Explore advanced concepts in tame control theory, focusing on phenomena over real fields. Delve into graduate-level mathematical analysis and applications.
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1 Lesons
1 hour 37 minutes
On-Demand
Free-Video
Fields Institute

Tame Phenomena Over the Real Field - Graduate Course Lecture 1

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Explore fundamental concepts of tame control theory, focusing on real field applications and advanced mathematical principles in this graduate-level lecture.
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1 Lesons
46 minutes
On-Demand
Free-Video
Society for Industrial and Applied Mathematics

Exploring the World of Coupled Oscillators - Jürgen Moser Lecture

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Pioneering insights into nonlinear systems and oscillatory dynamics, exploring emergent phenomena, synchrony, and chaos. Retrospective on key contributions to the field of coupled oscillators and dynamical reduction.
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1 Lesons
47 minutes
On-Demand
Free-Video
Fields Institute

Discovering Dynamics and Parameters of Nonlinear Systems from Partial Observations

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Explore techniques for uncovering nonlinear system dynamics and parameters using incomplete data, enhancing understanding of complex systems and their behavior.
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1 Lesons
23 minutes
On-Demand
Free-Video
Instituto de Física Interdisciplinar y Sistemas Complejos (IFISC)

Path Integral Control Theory

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Explore path integral control theory, a powerful mathematical framework for optimal control in complex systems. Gain insights into its applications and mathematical foundations.
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1 Lesons
4 hours 12 minutes
On-Demand
Free-Video
Instituto de Física Interdisciplinar y Sistemas Complejos (IFISC)

Artificial Neural Networks Through the Lens of Dynamical Systems Theory

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Explore artificial neural networks from a dynamical systems perspective, gaining insights into their behavior and properties.
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1 Lesons
25 minutes
On-Demand
Free-Video
ADC - Audio Developer Conference

Recent Trends in Virtual Analog Modeling Based on Nonlinear Wave Digital Filters

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Explore recent advancements in virtual analog modeling using nonlinear Wave Digital Filters. Gain insights into emulating complex audio circuits with multiple nonlinearities for improved stability, accuracy, and efficiency.
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1 Lesons
46 minutes
On-Demand
Free-Video
Institut des Hautes Etudes Scientifiques (IHES)

Stable Adaptation and Learning in Nonlinear Systems and Neural Networks

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Explore nonlinear systems tools for insights on collective computation and learning in large dynamical networks, focusing on stable adaptation and implicit sparse regularization.
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1 Lesons
35 minutes
On-Demand
Free-Video
ICTP-SAIFR

Introduction to Evolutionary Game Theory - Classes 3 and 4

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Explore evolutionary game theory applications in socio-economic complexity through advanced concepts and mathematical models.
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1 Lesons
1 hour 34 minutes
On-Demand
Free-Video
GERAD Research Center

Nonlinear Stochastic Hybrid Optimal Control with Fixed Terminal States

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Explore novel approaches for stochastic systems with fixed terminal states. Learn about Terminally Constrained Stochastic Minimum Principle and Hamilton-Jacobi equations for optimal control.
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1 Lesons
48 minutes
On-Demand
Free-Video
GERAD Research Center

Equivalence Between Contraction and Koopman Approaches and Its Application in Nonlinear System Identification

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Explore connections between Koopman operator and contraction analysis frameworks for nonlinear systems. Learn a new data-driven method for stable model learning using Koopman embeddings.
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1 Lesons
54 minutes
On-Demand
Free-Video
Society for Industrial and Applied Mathematics

Adaptive Regularization and Linearization for Nonsmooth and Degenerate Problems

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Explore advanced mathematical techniques for solving nonsmooth and degenerate problems in flow and transport, focusing on adaptive regularization methods and Newton-based linearization approaches.
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1 Lesons
59 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Introduction to Dynamical Systems - Lecture 1

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Explore dynamical systems, from linear ODEs to nonlinear chaos. Learn about equilibrium points, eigenvalues, attractors, and bifurcations. Gain insights into Lorenz systems, Poincaré maps, and iterative methods.
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25 Lesons
1 hour 14 minutes
On-Demand
Free-Video
ICTP Mathematics

Dynamical Systems - Lecture 02

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Explore advanced concepts in dynamical systems theory, focusing on mathematical principles and applications in complex systems analysis and modeling.
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1 Lesons
1 hour 30 minutes
On-Demand
Free-Video
ICTP Mathematics

Dynamical Systems - Lecture 03

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Explore advanced concepts in dynamical systems theory, focusing on mathematical principles and applications in complex systems analysis and modeling.
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1 Lesons
1 hour 27 minutes
On-Demand
Free-Video
ICTP Mathematics

Dynamical Systems - Lecture 04

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Explore advanced concepts in dynamical systems theory, focusing on mathematical principles and applications in complex systems analysis and modeling.
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1 Lesons
1 hour 22 minutes
On-Demand
Free-Video
ICTP Mathematics

Dynamical Systems - Lecture 01

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Explore fundamental concepts and applications of dynamical systems theory in this comprehensive lecture by mathematician Stefano Luzzatto.
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1 Lesons
1 hour 25 minutes
On-Demand
Free-Video
Steve Brunton

Numerical Simulation of Ordinary Differential Equations - Integrating ODEs

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Explore numerical integration of ODEs to analyze nonlinear systems and generate trajectories. Learn techniques for solving complex dynamics where analytic methods fall short.
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1 Lesons
24 minutes
On-Demand
Free-Video
Steve Brunton

Linearizing Around a Fixed Point - Control Bootcamp

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Explore linearization of nonlinear systems around fixed points, demonstrated with a simple pendulum example using both manual calculations and MATLAB implementation.
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1 Lesons
31 minutes
On-Demand
Free-Video
Instituto de Matemática Pura e Aplicada

Structure of Feigenbaum Henon Maps

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Explore Feigenbaum Henon maps structure in dynamical systems with Mikhail Lyubich's conference talk, part of a broad meeting celebrating Marcelo Viana's 60th birthday at IMPA.
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1 Lesons
56 minutes
On-Demand
Free-Video
Conference GSI

Multisymplectic Unscented Kalman Filter for Geometrically Exact Beams

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Explore advanced filtering techniques for geometrically exact beam models using multisymplectic unscented Kalman filters in structural engineering applications.
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1 Lesons
16 minutes
On-Demand
Free-Video
Institut Henri Poincaré

Fluctuation Limits for Mean-Field Interacting Nonlinear Hawkes Processes

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Explore fluctuation limits in mean-field interacting nonlinear Hawkes processes, delving into advanced mathematical concepts and their applications.
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1 Lesons
40 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Capturing Turbulent Dynamics and Statistics in Experiments Using Exact Coherent States

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Explore turbulent dynamics using Exact Coherent States, revealing coherent structures in experiments, forecasting turbulent evolution, and providing a geometric description of transient turbulence.
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29 Lesons
1 hour 10 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Application of Particle Filters on Data Assimilation

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Explore particle filters in data assimilation, a powerful technique for integrating observations and forecasts to estimate atmospheric states and uncertainties in weather and climate modeling.
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1 Lesons
1 hour 26 minutes
On-Demand
Free-Video
Institut des Hautes Etudes Scientifiques (IHES)

Mathematical General Relativity - Seventy-Two Years after Yvonne Choquet-Bruhat's Foundational Acta Paper

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Explorez les avancées majeures en relativité générale mathématique depuis l'article fondateur d'Y.C. Bruhat, en examinant son impact durable sur le domaine.
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1 Lesons
1 hour 12 minutes
On-Demand
Free-Video
Fields Institute

Exploring Nonlinearity: From Superconductivity to Quantum Sensing

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Discover nonlinear phenomena in superconductivity and quantum sensing, exploring cutting-edge research and applications in quantum information and control.
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1 Lesons
29 minutes
On-Demand
Free-Video
Cambridge University Press

Dynamics and Steady State of Squirmer Motion in Liquid Crystal

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Analyse mathématique du mouvement des micro-nageurs dans les cristaux liquides, établissant l'existence d'états stables et dérivant un modèle homogénéisé pour la nage collective.
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1 Lesons
10 minutes
On-Demand
Free-Video
Instituto de Física Interdisciplinar y Sistemas Complejos (IFISC)

Partisan Voter Model: Noise-Induced Transitions

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Explore noise-induced transitions in partisan voter models, examining complex dynamics and implications for opinion formation and social systems.
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1 Lesons
24 minutes
On-Demand
Free-Video
ICTP-SAIFR

Multi-agent Models in Complex Networks - Class 4

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Explore multi-agent models in complex networks, focusing on applications to socio-economic complexity and nonlinear systems.
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1 Lesons
37 minutes
On-Demand
Free-Video
Cambridge Materials

A Touch of Non-Linearity: Mesoscale Swimmers and Active Matter in Fluids

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Explore mesoscale swimmers and active matter in fluids, focusing on the transition from Stokes to intermediate Reynolds numbers and its impact on hydrodynamic interactions and collective behavior.
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1 Lesons
25 minutes
On-Demand
Free-Video
The Julia Programming Language

Solving Difficult Reachability Problems in JuMP.jl

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Explore advanced reachability analysis techniques for complex control systems using JuMP.jl, including temporal refinement and tools for nonlinear systems with neural network controllers.
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1 Lesons
13 minutes
On-Demand
Free-Video
DataLearning@ICL

Neuromancer: Differentiable Programming Library for Data-driven Modeling and Control

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Explore NeuroMANCER, an open-source library for integrating machine learning with scientific computing, solving optimization problems, and creating differentiable models with physics-based constraints.
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1 Lesons
59 minutes
On-Demand
Free-Video
BIMSA

Vortex Reconnection in the 3D Critical Abelian Higgs Model

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Explore vortex reconnection in 3D critical Abelian Higgs model, focusing on dynamics of nearly parallel vortex filaments and their collisions in particle physics.
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1 Lesons
58 minutes
On-Demand
Free-Video
ICTP-SAIFR

Economic and Financial Networks: Models and Analysis - Class 3

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Explore economic and financial network models and analysis techniques in this advanced lecture on nonlinear systems in socio-economic complexity.
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1 Lesons
47 minutes
On-Demand
Free-Video
ICTP-SAIFR

Time Series Analysis - Class 4

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Explore advanced time series analysis techniques in socio-economic complexity, focusing on nonlinear systems applications and cutting-edge research insights.
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1 Lesons
59 minutes
On-Demand
Free-Video
ICTP-SAIFR

Economic and Financial Networks: Models and Analysis - Class 4

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Explore advanced models and analysis techniques for economic and financial networks in this final session of a comprehensive series.
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1 Lesons
50 minutes
On-Demand
Free-Video
Alan Turing Institute

Kalman-Bucy Informed Neural Networks for System Identification

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Combining physics-informed neural networks and Kalman filters to identify parameters in continuous-time systems with noisy measurements, improving model precision for complex systems.
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1 Lesons
1 hour 1 minute
On-Demand
Free-Video
ICTP-SAIFR

Time Series Analysis - Class 3 of 4

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Explore advanced time series analysis techniques for socio-economic complexity in this comprehensive lecture by Cristina Masoller.
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1 Lesons
1 hour 2 minutes
On-Demand
Free-Video
Inside Livermore Lab

Challenges and Opportunities for Integrating Physics-Knowledge in Machine Learning Strategies

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Explore integrating physics knowledge into machine learning algorithms for improved generalization and physics-consistent predictions. Examine biases and strategies through a friction identification case study.
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1 Lesons
1 hour 10 minutes
On-Demand
Free-Video
Center for Language & Speech Processing(CLSP), JHU

Cellular Cooperation in Cochlear Mechanics

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Explore contrasting views of cochlear mechanics, including Hopf bifurcations and 3-D simulations, to understand nonlinear cochlear responses and their implications.
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1 Lesons
1 hour 11 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Dynamical Systems and Reservoir Computing - Lecture 2

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Delve into dynamical systems and reservoir computing applications in climate networks, focusing on analysis methods, bifurcation behavior, and network characterizers for climate data organization.
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1 Lesons
29 minutes
On-Demand
Free-Video
ChariotSolutions

Critical Shifts in Thinking for the Systems Age

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Explore how modern software development requires fundamental shifts in thinking patterns, moving from mechanistic approaches to systems-based perspectives for creating resilient digital solutions.
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1 Lesons
59 minutes
On-Demand
Free-Video